FINDING THE SQUARE ROOT OF THE NUMBER WITHOUT USING A CALCULATOR.

         Since √1 = 1 and √100 = 10, the square root of any number lying between 1 and 100 must lie between 1 and 10 i.e. the square root of a number of one and two digit is a number of one digit.
          Similarly, since √100 = 10 and √10000 = 100, the square root of any number lying between 100 and 10000 must lie between 10 and 100 i.e. the square root of a number of 3 or 4 digits is a number of 2 digits.
          Similarly, the square root of a number of 5 or 6 digits is a number of 3 digits and so on.
          Hence, if the digits of a given number are marked off in group of two starting from the right, the number of groups will show the number of digits that there will be in the square root.



The successive steps are 1. Mark off the digits from the right in group of two 2. Find the largest number whose square is not greater than 40 i.e. 6 3. Put 6 in the working above the 40 and also as divisor 4. Multiply 6 by 6, subtract the result which is 36 from 40 leaving 4 and bring down the next group i.e. 57. 5. Double the 6 on the top line and put down 12 as the first part of the next divisor which will be one hundred and something i.e. 124 × 4 =496 which is greater than 457 but 123 × 3=369. 6. Put 3 in the top line above the 57 and also after the 12 in the divisor to complete the 123.Multiply 123 by 3, subtract and bring down the next group i.e. 69. 7. Double the 63 on the top line and put down 126 as the first part of the next divisor which will be 126* and * i.e. 1267 × 7 = 8869 which is equal to the number to divide. 8. Put 7 in the top line above the 69 and also after the 126 in the divisor to complete the 1267.Multiply 1267 by 7, subtract and there is no remainder.

NOTE: The last group on the left hand side may consist of only one digit.

Author: Ayoola John or linkdin